One gain mechanism: frames analysed in their own units, the gain applied where a photon count is assumed

The gain of an input in detector units (SMV, marCCD, XTC, the XFEL formats) is measured once, before
anything reads the frames (RugnuxMeasureGain: photon-peak spacing and background variance per unit
mean), or given with --gain, and handed to the integration and the spot finding by one function
(ApplyRugnuxPixelGain). The rotation pre-scan no longer measures it, and the stills reader no longer
converts frames of a detector whose photons are not resolved: SACLA MPCCD, Rayonix and CCD frames are
integrated in ADU at the gain, rotation and stills alike.

Where a photon count was assumed, it is now taken at the gain (bit-identical at gain 1):
- integration: the background clip's one-photon floor, the sigma floor (one photon), the profile fit's
  background floor (0.01 photon), and a still's overload kept as a lower bound, which was left in ADU
  while every other reflection left the integrator in photons - the cause of the earlier loss of the
  engine route on clipped CCD stills (merged low resolution inflated by the gain, the rocking-width
  fit's bandwidth collapsing); CPU and CUDA, Metal through the shared CPU code;
- the adaptive spot threshold (Poisson arm and its one-photon floor), CPU and GPU;
- the pre-scan spot-width measurement (strong-spot SNR, the ring clip) behind the stills bandwidth and
  the rotation signal radius;
- the hot/dead pixel tests, CPU and GPU; the empty-aperture ring clip.
BackgroundPixelGain is gone: one pixel_gain.

A detector whose background resolves single photons (photon peaks: JUNGFRAU in keV, AGIPD) is a photon
counter and its frames are still counted in whole photons as read: analysed in keV at the gain instead,
a photon-counting still set lost 0.008 R-free (fewer spots, a noisier beam-centre trial) - the rounding
is the detector's own discrimination. --gain sets the value, the background still says which kind.

Validation, against rc178: photon-counting and g<=1 rotation p.hkl md5-identical (lyso, thau, cytc,
myob, insu, a small-molecule set, 5reo, 6cee, 6i3j, 2xfw, 6s1u, 8v4j); CCD g>1 at or within noise of rc178 (5uth
R_meas 0.113 -> 0.108). Stills R-free (0-cycle REFMAC): MPCCD sets 0.184 -> 0.185 and 0.199 -> 0.196,
Rayonix identical, photon-resolving sets back on their rc178 numbers.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015CeEGgpKdfkCTJb3YNMJcu
(cherry picked from commit da8dbfc8147354b63e375f2d9521dffb80938b6d)

image_analysis/bragg_integration/BraggIntegrationEngine.cpp

@@ -117,7 +117,6 @@ BraggIntegrationEngine::BraggIntegrationEngine(const DiffractionExperiment &expe
     // symmetric trimmed mean (rugnux --background-trim). The caller owns the choice - the engine no
     // longer overrides it for broadband data.
     bkg_clip_nsigma = settings.GetBackgroundClipNSigma();
-    bkg_pixel_gain = settings.GetBackgroundPixelGain();
     pixel_gain = settings.GetPixelGain();
     bkg_trim = bkg_clip_nsigma > 0.0f ? 0.0f : settings.GetBackgroundTrimFraction();
 
@@ -290,9 +289,11 @@ std::vector<Reflection> BraggIntegrationEngine::Finalize(const std::vector<Refle
         // this frame has nothing to count at the limit, and counting those pixels as zero is no
         // lower bound of anything - it stays overloaded and is dropped. (A pixel stuck at the limit
         // is no clipped spot either; the pre-scan masks it, HotPixelFinder.)
+        // Counted in ADU like everything else, its own variance at the gain, then in photons.
         if (fr.overloaded && keep_overloads && fr.saturated > 0) {
-            refl.I = fr.I + static_cast<float>(fr.saturated * (saturation_limit - fr.bkg));
-            refl.sigma = std::sqrt(fr.var_bkg + std::max(refl.I, 1.0f));
+            const float I = fr.I + static_cast<float>(fr.saturated * (saturation_limit - fr.bkg));
+            refl.I = I / pixel_gain;
+            refl.sigma = std::sqrt(fr.var_bkg + pixel_gain * std::max(I, pixel_gain)) / pixel_gain;
             refl.overloaded = false;
             ++counts.overloads_kept;
         }